Following up on this, we identified the user action when the Right Click-Download link is selected, which is:

and tested it in the console, and got our downloads. We will link that line to a button/icon we put on the page.

Next, we'd like to show the download icon only if the user has selected an item, and hide it if there are no items selected. 

When you select an item, the row is highlit:

If we can detect the presence of the class that does the highlight, it will act as a proxy for selected/not selected.  Problem is, we are not seeing the class that is called.  Is this in an externally referenced page? Or can anyone identify the class?

As a last resort we could iterate through all of the check boxes but that does not seem like a terribly efficient solution.